The important thing is for those who know better to correct false claims. The issue with this is that the user in question simply ignores any corrections, and continues on, posting the same nonsense over and over. Your continued efforts are appreciated :)

"Or are you content to post some nonsense, then whine when you're not taken seriously rather than using that time instead to learn something so that you can do better in the future?"

Exactly this. A short, if depressing delve into this users post history will show this exact behaviour. Post nonsense, get called out for said nonsense, play the victim, contradictory behaviour, learn nothing, lather, rinse and repeat.